Concept

Préconditionneur

Publications associées (114)

Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates

Quasi-Newton (qN) techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other quasi-Newton schemes, ...

MICROTOME PUBLISHING2021

A hierarchical preconditioner for wave problems in quasilinear complexity

Jan Sickmann Hesthaven, Boris Bonev

The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property th ...

2020

Least-Squares Padé approximation of parametric and stochastic Helmholtz maps

Fabio Nobile, Francesca Bonizzoni, Davide Pradovera

The present work deals with rational model order reduction methods based on the single-point Least-Square (LS) Padé approximation techniques introduced in Bonizzoni et al. (ESAIM Math. Model. Numer. Anal., 52(4), 1261–1284 2018, Math. Comput. 89, 1229–1257 ...

2020

On the choice of metric in gradient-based theories of brain function

Wulfram Gerstner, Johanni Michael Brea, Jean-Pascal Théodor Pfister

The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Because a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need to be made to ...

2020

Multi space reduced basis preconditioners for parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

We introduce a two-level preconditioner for the efficient solution of large scale saddle point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (M ...

PERGAMON-ELSEVIER SCIENCE LTD2019

SparseFool: a few pixels make a big difference

Pascal Frossard, Seyed Mohsen Moosavi Dezfooli, Apostolos Modas

Deep Neural Networks have achieved extraordinary results on image classification tasks, but have been shown to be vulnerable to attacks with carefully crafted perturbations of the input data. Although most attacks usually change values of many image's pixe ...

IEEE2019

Trajectory Optimization for Legged Robots With Slipping Motions

Marco Hutter

The dynamics of legged systems are characterized by under-actuation, instability, and contact state switching. We present a trajectory optimization method for generating physically consistent motions under these conditions. By integrating a custom solver f ...

2019

Diffusion Learning In Non-Convex Environments

Ali H. Sayed, Stefan Vlaski

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, recent years have seen rising interest in the behavior of gradient-descent based algorithms in non-convex environments. Most of the works on d ...

IEEE2019

MATHICSE Technical Report : Multi space reduced basis preconditioners for parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

In this work we introduce a two-level preconditioner for the efficient solution of large scale saddlepoint linear systems arising from the finite element (FE) discretization of parametrized Stokes equations.The proposed preconditioner extends the Multi Spa ...

MATHICSE2018

Multi space reduced basis preconditioners for parametrized partial differential equations

Niccolò Dal Santo

The multiquery solution of parametric partial differential equations (PDEs), that is, PDEs depending on a vector of parameters, is computationally challenging and appears in several engineering contexts, such as PDE-constrained optimization, uncertainty qu ...

EPFL2018

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